Draw Polygons & Compound Figures with a Given Area using Pro-Bot

Can you program the Pro-Bot to draw polygons & compound figures with a given area?

This, again, is an assignment that I designed for our Grade 3 students. It relates to the Common Core Math Standards: Geometric measurement: understand the concepts of area. For this exercise, I highly recommend using graph paper, as it provides a helpful medium for the kids to work out the math problems. Provide at least one sheet per child to work out the problem and then additional sheets as required for the groups to draw the figures using Pro-Bot. Here is a link to a graph paper with 1 cm grid in PDF format; you can make copies for the students to draw on using the Pro-Bot.

Area of a Figure

The area of a figure is the number of squares required to cover it completely, and is specified in square units. Here's an article from math.com that gives a quick overview of the topic.

How do you calculate the area of a given figure? You add the number of squares needed to cover the entire figure. Say you are given a square with sides 3 cm each. You need 9 squares of sides 1 cm x 1 cm to cover it completely. The area of the square is 3 x 3 = 9 sq.cm. Similarly, a 5 cm x 6 cm rectangle has an area of 30 sq.cm.

Can we do the reverse too? Given the area, can we come up with the design for a figure with that area? 

Let's look at an example. Given an area of 9 sq.cm, how many polygons can we draw? We can draw multiple polygons, all with the exact same area of 9 sq.cm. In the figure below, you can see:

• a square 3 cm x 3 cm,
• couple of polygons with an area of 9 sq.cm.

Can you think of more polygons with an area of 9 sq.cm?

Let's now look at a scenario that shows the practical application of the concept of area. And then program the Pro-Bot to draw a few polygons with a given area.

Programming Assignment

You work for an architectural firm, and have been asked to design a single story house with a floor area of 100 square meters (roughly 1076 sq.ft.) You are to draw and present various designs for the floor plan.

1. How many different ways can you draw the floor plan with an area of 100 sq.m.? Provide at least 2 to 3 different designs and make a rough drawing of the figures that you come up with.

2. Classify the figures that you came up with into the various classes of polygons based on the number of sides.

3. Program the Pro-Bot to draw them on graph paper. Use 1 sq.cm. to represent 1 sq.m. in your figures.

4. Assume that the plot of land available for the construction, is a rectangle that is 15 m long and 8 m wide. Can you provide a design(s) to build a 100 sq.m. building in this plot? Program your Pro-Bot to draw the design. 
5. You can program the Pro-Bot to draw other figures with the 100 sq.m. area. Or explore other figures with different areas.

Draw Polygons with a Given Perimeter using Pro-Bot

Can you program the Pro-Bot to draw polygons & compound figures with a given perimeter?

This is an assignment that I designed for our Grade 3 students. It relates to the Common Core Math Standards: Geometric measurement: recognize perimeter. For this exercise, I highly recommend using graph paper, as it provides a helpful medium for the kids to work out the math problems. Provide at least one sheet per child to work out the problem and then additional sheets as required for the groups to draw the figures using Pro-Bot. Here is a link to a graph paper with 1 cm grid in PDF format; you can make copies for the students to draw on using the Pro-Bot.

Perimeter of a Figure

A perimeter is a path that surrounds a two-dimensional shape. The term may be used for either the path or its length. It can be thought of as the length of the outline of a shape. (Wiki)

How do you calculate the perimeter of a given figure? You add the length of all the sides of that figure that form its outline. Say you are given a square with sides 3 cm each. The perimeter of the square is 3 + 3 + 3 + 3 = 12 cm. Similarly, a 5 cm x 6 cm rectangle. has a perimeter of 5 + 6 + 5 + 6 = 22 cm. 

Can we do the reverse too? Given the perimeter, can we come up with the design for a figure with that perimeter? 

Let's look at an example. Given a perimeter of 12 cm, how many polygons can we draw? We can draw multiple polygons, all with the exact same perimeter of 12 cm. In the figure below, you can see:

• a square 3 cm x 3 cm,
• a rectangle 5 cm x 1 cm,
• a rectangle 4 cm x 2 cm,
• a hexagon with sides 3 cm, 1 cm, 1 cm, 1 cm, 4 cm, 2 cm

Can you think of more polygons with a perimeter of 12 cm?

Let's now look at a scenario that shows the practical application of the concept of perimeters. And then program the Pro-Bot to draw a few polygons with a given perimeter.

Programming Assignment

Old McDonald lives on a farm and has lots of animals. He would like to build a new set of fences to keep his cows safe.

1. If Old McDonald has 36 meters of fencing available, how many different ways can he build an enclosed area for his cows? Make a rough drawing of the figures that you come up with and then program the Pro-Bot to draw them on graph paper. Use 1 cm to represent 1 m in your figures.
2. Classify the figures that you came up with into the various classes of polygons based on the number of sides.
3. Write programs for Pro-Bot to draw at least 3 of the figures that you came up with.
4. Suppose Old McDonald has only 35 meters of fencing available, but wants to build a square or rectangular fence using all of that fencing material. Would it be possible for him to build it? Why or why not? 
5. You can program the Pro-Bot to draw other figures with the 36 cm perimeter. Or explore other figures with different perimeters.

Doodle Pencil - Using the Pen & Mouse Pointer Coordinates in Scratch

Here's a fun little Doodler made with Scratch:  The Doodle Pencil
















This was rather a spur-of-the-moment project... inspired by Etch-a-Sketch...  and kind of a follow-up on the Pac-Man game...

The code is minimal, and I feel not much of an explanation is required. The instructions are mainly from the Pen area of the Scratch Instruction Set, along with the instruction to follow the mouse-pointer. The "green flag click" handler does the initialization - clearing the screen, setting the sprite size and setting up the pen size & color.

The code is interactive, and it's designed to enable the user to lift and lower the pen as required while doodling: Move the mouse pointer to the desired location on screen and then click on the up arrow key; the pen will start drawing now by following the movements of your mouse pointer. Click on the down arrow key to stop drawing at any point.

This could be a fun little exercise for the kids to see how different combinations of the "Pen" and "Motion" instructions interact with each other.

Enjoy doodling!

CopyCat - A Simple Intro to User Input and Variables via Scratch

My child and I worked on CopyCat as a simple introduction to variables and user input in Scratch. Algebra is part of the Grade 4 Math curriculum in the USA, and this project could be a fun way to introduce the use of variables.

Aim:  

Design an interactive game in Scratch, where a CopyCat copies/repeats everything that you type in.

The Design Process:

• Only a single sprite is required: the CopyCat. You can either choose from the list of sprites already available on Scratch, or draw your own. 

• To provide user interaction in starting and stopping the game, we used the "green flag click" to start and the "space key click" to stop the game (both of which can be found under the section "Events" in the Scripts area in Scratch). You can choose any of the options that are available in "Events" to do the same.

Various sections in the Scripts area of Scratch

And now the fun part: CopyCat needs to copy everything that you type in.
How can we achieve this?

• Under "Sensing" in the Scripts area in Scratch, you will find a block that asks for user input and waits for it. This is what we shall use, to ask the user to type in anything they like.

• Once the user input is received, CopyCat needs to repeat it. But, how can CopyCat remember what the user typed in? Here is where the concept of variables comes into play. In the section "Sensing", you will find the variable "answer", which stores whatever the user typed in. 

• I recommend selecting the box right next to "answer", so that it is visible on the screen and the kids can see how its value varies (hence the name variable), depending on the user input.

• The CopyCat can now use this variable along with the "say" instruction (found in the "Looks" area of Scripts in Scratch), to repeat/copy whatever the user types in.

Ask the students to try writing the code upto this point:

1. When "green flag clicked" (or other event), CopyCat asks the user to type in something.
2. CopyCat repeats the user input, via the variable "answer". 
3. When "space key clicked" (or other event), stop the program.

Let the students experiment with different values for the user input and observe how the variable changes accordingly. Once comfortable with the use of the variable, they can hide it by deselecting the box next to "answer".  It would be good to remind the students at this point, that this feature is helpful for debugging.

Here are three screen shots to demonstrate how the user input gets stored in the variable "answer".

  Asking for user input; variable is empty

User input entered; variable is empty till Return key is pressed

User input is now stored in the variable

Pac-Man is Chasing my Planet!

My child's class was recently introduced to Cartesian coordinates in Math. And in our coding class, we have been practicing interactive programming for the last few weeks. So, I thought of putting together a very simple template that  combines both the concepts, that the kids could then remix...  Pac-Man is Chasing my Planet! was the result... took me less than 10 minutes to put together and the kids loved it.

We went through the Pac-Man template code as a group & discussed the use of the XY coordinates. I showed the kids how the XY coordinates displayed under the Scratch animations area change, as I move the cursor around on the screen. Our discussion then proceeded along the following lines:

• If I wanted my sprite (the planet, in this case) to move anywhere the cursor moves, what values should I use for the sprite's X and Y coordinates? 
• The above point was also a good place to talk about variables, and how the change of the cursor position is always reflected in the planet's position. 
• Should I move the planet around for just a few times or all the time? What kind of a loop should I use here?
• How can I make Pac-Man always follow the planet? Which loop should I use? 
• What values should I use for Pac-Man's X and Y coordinates? 
• Here, the kids quickly saw that without a small degree of separation between the coordinate values of the planet & Pac-Man, the two sprites overlap each other.
• BTW, the "if-else" clause was purely optional, for those to wanted to add another level to their game. The majority went with just a "go to x() y()"
• And finally, the interactive part of the game... I put in the requirement that there should "a key press" or "the green flag click" to make the game start, and something similar to end the game. 

In the next one hour, the children came up with multiple variations of the game, making their own sprites and designing various versions of tag... All in all, a very fun class for them and me to wrap up the school year.

Happy Summer!!

A Drive through the Zoo: Learning about Angles using Pro-Bot

My child's class started learning about angles about a week ago. And the teacher requested me to design an exercise for Pro-Bot that will introduce the idea of angles. As the kids are very new to the concept, I wanted to keep this one fairly simple, while still using a mix of acute, obtuse and right angles.

A trip to the zoo is almost always part of our field trips every school year. The zoo in our city happens to have buses that drive along the various points of interest/ themed animal enclosures. I felt that the turns made by the bus in this familiar setting of the zoo, might be a good way to introduce angles.

In this exercise, a scaled down version of the bus route, provides the path for Pro-Bot to drive on. As the Bot drives along the path, it is required to make angular turns at each point. I have provided the angular measurements required in degrees and distances in centimeters. The bus travels in a loop, the directions are shown using arrows. Note that the map below is not drawn to scale.

Based on the above map, write a program for Pro-Bot to drive along the following paths, assuming that the Pro-Bot is facing in the forward direction:

1. The path from the Entrance of the zoo to the African Savanah. How many turns did the Pro-Bot make? Were the angles acute, obtuse or right angles?
2. To continue from the African Savanah (where you stopped before), to the Elephants enclosure, how many degrees did the Pro-Bot turn? 
3. Program the path from the African Savanah to the Raptors. How many turns did the Pro-Bot make? Were the angles acute, obtuse or right angles?
4. Continue the path from the Raptors to the Kids' Play Area. Did you use acute, obtuse or right angles for the turns?

Alternatively, the kids can be asked to program the entire bus route as a single program, marking the types of angles used along the way.

Traveling Pro-Bot: Finding the shortest path

The Traveling Salesman Problem is one of the most famous and one of the most complex in Computer Science. The problem can be cited as the following: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the starting city? 

This problem in its various forms has a variety of applications in multiple fields for optimization purposes. For example, a school district would like to find the best route for a school bus to pick up kids in the morning. The courier company would like to determine the best route to drop off packages, with minimum fuel costs. In a factory assembly line, if you can find a way to visit all the required stations in minimal time, you can manufacture more units in a day. There are several more instances of the application of this problem and the “cities” in the original problem will denote various points in those instances. As the number of “cities” increases, the complexity of the problem also increases.

We shall work on a very simple instance of the above problem, involving a maximum of just 5 cities. Pro-Bot shall represent our salesman, driving between the various cities.

Computer Science concepts involved:  Sequential programming, A peek into optimization techniques

Math concepts involved:  Using data given for creating a graph, Measuring distances and directions on a map, Finding shortest path, Cost comparison, Measuring angles, Scaling quantities 

Grade levels:  4, 5

Hours required:   2 or more

Distance between cities in miles
The distances between the various cities are given in the table below in miles. Note that these are straight line distances between the cities (as the crow flies) and not driving distances. 

                     City Name                            City Name                      Distance in miles

On a map of USA, locate the various cities given in the table above. 

Task 1
We shall start with a very simple route. Let’s consider the three cities of San Diego, Austin and Denver. Pro-Bot has to visit all three cities, starting from San Diego and returning to San Diego. No city other than San Diego should be visited more than once. What order should the cities be visited in so that the total distance traveled is minimized?

Remember that the minimum distance Pro-Bot can draw is 1cm. Given the distances in the table above and using a scale of 1 cm to represent 100 miles, can you round the distances so that they can be used by Pro-Bot?  Draw a small graphical representation of your cities and distances between them as shown below. This might be helpful for you to visualize the problem. 

Using  a map of the USA and a protractor, try to find out the angular measurements between the various cities (approximate values are fine). Using the distance and angular information, as well as the location of the various cities on the map, can you write a program for Pro-Bot to visit all three cities, starting and ending at San Diego?

If gas costs $3 a gallon and Pro-Bot uses one gallon per 10 miles, how much did it cost for the trip?

Task 2
We shall move on to a route that involves 4 cities now: San Diego, Austin, Denver and Chicago. Pro-Bot has to visit all four cities, starting from San Diego and returning to San Diego. No city other than San Diego should be visited more than once. What order should the cities be visited in so that the total distance traveled by Pro-Bot is minimized? 

Remember that the minimum distance Pro-Bot can draw is 1cm. Given the distances in the table above and using a scale of 1 cm to represent 100 miles, can you round the distances so that they can be used by Pro-Bot?  Draw a small graphical representation of your cities and distances between them as we did in the previous task. This might be helpful to visualize the problem.

Using  a map of the USA and a protractor, try to find out the angular measurements between the various cities (approximate values are fine). Using the distance and angular information, as well as the location of the various cities on the map, can you write a program for Pro-Bot to visit all four cities, starting and ending at San Diego, so that the total distance traveled is kept to a minimum?

If gas costs $3 a gallon and Pro-Bot uses one gallon per 10 miles, how much did it cost for the trip?

Task 3
We shall work on a route that involves 5 cities now: San Diego, Austin, Denver, Chicago and Las Vegas. Pro-Bot has to visit all five cities, starting from San Diego and returning to San Diego. No city other than San Diego should be visited more than once. What order should the cities be visited in so that the total distance traveled by Pro-Bot is minimized? 

Remember that the minimum distance Pro-Bot can draw is 1cm. Given the distances in the table above and using a scale of 1 cm to represent 100 miles, can you round the distances so that they can be used by Pro-Bot?  

Using  a map of the USA and a protractor, try to find out the angular measurements between the various cities (approximate values are fine). Using the distance and angular information, as well as the location of the various cities on the map, can you write a program for Pro-Bot to visit all four cities, starting and ending at San Diego, so that the total distance traveled can be kept to a minimum?

If gas costs $3 a gallon and Pro-Bot uses one gallon per 10 miles, how much did it cost for the trip?

A few points to think about:

• As you worked on the above 3 tasks, did you notice that as the number of cities increased, your job of finding the route with minimum cost also became more complex?
• Was there a particular technique that you used for finding the  minimum cost route in each case? 
• Or did you evaluate all possible routes in each task and then choose the best one to write your program for? Do you think that it would be a good solution for a large number of cities, say 1000 or 10,000 or so?
• Can a change in constraints lead to a change in the routes that you found? Check the next section for an example.

A Different Condition & A Different Route:

Now, imagine that Pro-Bot is a rental car that you picked up at the San Diego airport. You shall use Pro-Bot to visit various cities starting from San Diego. We would still like to keep our distance and gas costs to a minimum and visit each city only once. But this time, Pro-Bot does not need to return to San Diego after visiting all the cities. You can it drop off at the last city that you visit. 

For each of the tasks above, does this change in the conditions cause a change in the route?

Task 4:
Pro-Bot visits San Diego, Austin and Denver, starting from San Diego. The distances between the cities and the gas prices are the same as before. You do not have to return to San Diego. Can you write a program for Pro-Bot’s route that involves the minimum gas cost? Is it the same route as in Task 1?

Task 5:
Pro-Bot visits San Diego, Austin, Denver and Chicago, starting from San Diego. The distances between the cities and the gas prices are the same as before. You do not have to return to San Diego. Can you write a program for Pro-Bot’s route that involves the minimum gas cost? Is it the same route as in Task 2?

Task 6:
Pro-Bot visits San Diego, Austin, Denver, Chicago and Las Vegas, starting from San Diego. The distances between the cities and the gas prices are the same as before. You do not have to return to San Diego. Can you write a program for Pro-Bot’s route that involves the minimum gas cost? Is it the same route as in Task 3?

Sensors in Pro-Bot: Relay Driving by Pro-Bots using Sensors

Pro-Bot has three kinds of sensors built into it: touch, light and sound sensors. Before we start writing programs for Pro-Bot that use the sensors, let’s see what purpose these sensors serve and what “sensing” means.

Sensing 

When someone taps your shoulder, how do you know you were touched? When the light bulb goes on in a dark room, how do you know the room suddenly got bright? When you put a candy in your mouth, how do you know that it is sweet? Because your skin sensed the touch, or your eyes sensed the light, or your tongue sensed the taste… Once you sense something, you typically react to it, don’t you? When you sense the touch, you may turn around to see who tapped your shoulder; when you sense the light coming on in the dark room, you may squint your eyes and try to figure out what is in that room; when you sense the sweetness on your tongue, you may feel happy and say “yummy”…

Your skin, eyes, tongue, etc., have “sensors” that sense some “stimulus” like touch, light, taste, etc., and enable you to respond to it. You may have also noticed that you have different sensors for different functions. Sensors are made to detect very specific stimuli. For example: your skin doesn’t see, you have eyes to do that; your eyes don’t taste the sweetness of the candy, you have taste buds on your tongue to do that.

Now what if a robot could behave similarly (it may not behave in exactly the same ways as you do)? A robot can be fitted with sensors and programmed to respond in a certain way when the sensor senses a stimulus.

Pro-Bot has 3 kinds of sensors - one senses light, one senses contact (or touch) on its front and rear bumpers and the other senses sound. Pro-Bot’s sensors must be turned on, if you want them to detect stimuli and respond to them (they are switched off by default). Think of it as needing your eyes to be open to see the light. The sensors detect only the specific stimuli that they are designed for. For example, the touch sensor or the light sensor on Pro-Bot will not detect or respond to sounds. They will respond only to touch and light stimuli respectively. However, short sharp sounds (like a loud clap or a short yell) may be detected by the sound sensor and you can program the robot to respond to it.

Now, how does Pro-Bot react when these sensors sense something? Consider the touch sensors on Pro-Bot’s front and rear bumpers. You can program Pro-Bot to do something when those sensors sense a contact (such as bumping into something, or getting bumped by something). Similarly, the light sensor on Pro-Bot can be programmed to do something when it detects a change in lighting.

Pro-Bot has 5 specialized Procedures that correspond to inputs from its sensors. These are 

33 FRONT

34 REAR

35 DARK

36 LIGHT

37 SOUND

You can access and modify the above Procedures via the Menu button on the control pad. The instructions in each of these Procedures will be executed when the the corresponding sensor detects a stimulus. If the Procedure corresponding to the sensor is empty (if you decide not to react to a stimulus), Pro-Bot does not respond to changes in the sensor condition. 

So, what happens after Pro-Bot has responded to a stimulus? Before you answer that question, consider this scenario: Imagine that you are sitting in your chair and reading a book. Your friend comes over, taps you on the shoulder and asks you something. Your skin’s touch sensor senses the tap, and your ears (another of your sensors), sense the spoken words. Maybe your friend was asking you to join her in a game. Let us say you respond saying “Later”. What do you do next? You would continue reading that interesting book, right? 

Let’s analyze what just happened. You were doing something… then you got “interrupted” by your friend… you “handled” that interruption… and then you got back to doing your reading… A computer or a robot can react the same way. When its sensor detects a stimulus, Pro-Bot can react to it by running a specific program, and after it is done, Pro-Bot continues with what it was doing before the interrupt happened. For example, if Pro-Bot was driving and midway, it entered a dark tunnel, it would detect the change in light and may turn on the headlights (if you programmed it to respond that way) and after that, it would continue driving along. After it is done with the response to the stimulus, Pro-Bot resumes the steps in the main program. 

What you have learned above is a fundamental behavior in Computer Science and Robotics: handling interrupts. 

Let us test our understanding now with an assignment that uses sensors.

Relay Driving by Pro-Bots using Touch Sensors:

Computer Science Concepts involved:   Procedures, Sensors to detect and react to stimuli, a quick peek into Interrupt handling

Math Concepts Involved:   Linear measurements, Solving real world problems by modeling with mathematics

Grade Levels:   3, 4, 5

Hours Required:   1

Materials Required:   A pre-set path drawn for the Pro-Bot to drive on, preferably marked with blue tape. Optionally, a shoebox with one vertical side cut open to act as a garage for Pro-Bot

Programming Assignment:

Let’s look at a simple task to start off with, involving 2 Pro-Bots. The steps are listed below.

1. Mark a path on the floor with blue tape that is about 40 cm long. You can also mark a target finish line at the end of the path.
2. Place one Pro-Bot at the beginning of the path, facing forward and ready to drive along the path. 
3. Place the second Pro-Bot at approximately the midpoint of the path, 20 cm away from the start point, facing forward and ready to start driving. (Both cars face the same direction.)
4. Optionally, place a ‘garage’ (made out of an upside down shoe box with one side cut for the car to enter) at the very end of the path.
5. Make sure that the sensors are set to "On" from the Menu button on Pro-Bot.
6. Program your Pro-Bots so that the first car starts driving along the path while the second car is waiting. The first car hits the back of the second car, makes a beep sound and stops. The second car now starts driving. It drives all the way into the finish line/ garage. It makes a beep sound and stops. (Optional step: when it gets inside the garage, it switches its headlights on.)

Now, how can we program the two Pro-Bots to do this?

• For the first Pro-Bot, the task involves driving forward, say 20 cm, to reach the second car and then reacting to a touch on the front bumper when it hits the second Pro-Bot. So, your program for the first Pro-Bot has to be split up into two parts - the Main program that handles the driving forward part and Procedure 33 FRONT that handles the contact to the front sensor. You will have to edit Procedure 33 FRONT to make the beep sound & add in a few Pause instructions to make the car stop.

• For the second car, driving starts only when it gets hit on the rear bumper. To make the car wait, your Main program shall have a few Pause instructions in a loop. You would also need to modify Procedure 34 REAR to make the car react to the hit on the rear bumper and drive to the finish line/ garage. Optionally, once inside the garage, the light sensor can detect the darkness and respond to it; for this modify the procedure 35 DARK to switch on the lights.

Once the two Pro-Bots have been programmed, press the GO button on both cars at the same time and watch the relay race happen! Here is a sample set of programs, for two Pro-Bots kept at a distance of 20 cm from each other and the finish line at a distance of 20 cm from the second Pro-Bot:

Pro-Bot 1:

• Main - Fd 20

• 33 FRONT -  Sound 3

                              Rpt 20 [

                              Ps

                              ]

Pro-Bot 2:

• Main - Rpt 20 [

                   Ps

                   ]

• 34 REAR -  Fd 20

                           Sound 3

• Optionally, 35 DARK - Light On

Note:   This project can be easily extended to include more cars and more complicated paths. Since we do not have a Stop instruction available, we can make the car stop by using the Pause instruction in a loop. 

Extension

If working on the relay race project with 3 or more cars, all the cars other than the first and last ones would need to handle both their front and rear touch sensors. Let’s look at an example with 3 cars, assuming they are kept at a distance of 20 cm each. In this case, the first car would behave as Pro-Bot 1 above and the last car would behave as Pro-Bot 2 above. Here is a sample set of programs for the 3 car relay race:

First  Pro-Bot :

• Main - Fd 20

• 33 FRONT -  Sound 3

                              Rpt 20 [

                              Ps

                              ]

Middle Pro-Bot:

• Main: Rpt 20 [

                  Ps

                  ]

• 34 REAR -  Fd 20

                           Sound 3

                                

• 33 FRONT -  Sound 3

                              Rpt 20 [

                              Ps

                              ]

Last Pro-Bot :

• Main - Rpt 50 [                     // Remember to make the Pro-Bot wait longer 

Ps // here to allow for the other two cars to catch up.

                   ]

• 34 REAR -  Fd 20

                           Sound 3

• Optionally, 35 DARK - Light On